Random roll modified by common sense, to a large extent, usually done by me as DM during downtime...unless the new PC is coming in at raw 1st-level, or is coming in as a rescued captive or slave (usually = no possessions at all). It is very rare in our crew that a player asks to have a specific item coming in, but if someone says "if I'm coming in with a magic weapon, can it be a battleaxe?" I'm cool with that. I'm not cool with them automatically assuming they'll come in with a magic weapon, though...
I assume the PC has had something of an adventuring career prior to meeting the party. Given that, and its level, I roll to see how wealthy it is relative to where it probably should be; simple fact of life that some characters come out richer than their peers, while others suffer mishaps and lose wealth hand over fist.
Then, I roll to roughly figure out how much of said wealth is magic, and how much is cash/gems/etc., heavily weighted toward the magic side. Then, given all this, I do some very generalized rolling (how lucky have they been in finding weapons? armour? potions? oddball stuff? etc.) and come up with some items the PC would reasonably have.
Looting dead party members (we call this "vampiring") is another issue entirely, and tough to adjudicate. A PC's posessions don't just vanish on death, so they have to go somewhere. Wills are only any use if the party abide by them...not guaranteed. Sometimes, the possessions get blown up by whatever killed the PC. Rarely (but I've seen it happen) a party Cleric will sacrifice some or all of a dead comrade's loot to some deity. But most often, the possessions just get plowed into party treasury, to be divided with the other loot next time in town.
Lanefan